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test: Add BLAS/LAPACK property tests, semiring laws; guard Graphics
- Expose ArrayFire.Exception and ArrayFire.Internal.Defines from the library - Add matmul/transpose/dot algebraic property tests in BLASSpec - Add QR/SVD/Cholesky reconstruction property tests in LAPACKSpec - Exercise semiringLaws/ringLaws via Scalar Semiring/Ring instances - Drop unguardable headless window tests from GraphicsSpec - Document degenerate createFeatures 0 accessor behavior Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
1 parent 4be8995 commit 83dd090

7 files changed

Lines changed: 156 additions & 45 deletions

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‎arrayfire.cabal‎

Lines changed: 3 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -41,6 +41,8 @@ library
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ArrayFire.Backend
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ArrayFire.BLAS
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ArrayFire.Data
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ArrayFire.Exception
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ArrayFire.Internal.Defines
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ArrayFire.Device
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ArrayFire.Features
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ArrayFire.Graphics
@@ -56,15 +58,13 @@ library
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ArrayFire.Vision
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other-modules:
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ArrayFire.FFI
59-
ArrayFire.Exception
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ArrayFire.Orphans
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ArrayFire.Internal.Algorithm
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ArrayFire.Internal.Arith
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ArrayFire.Internal.Array
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ArrayFire.Internal.Backend
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ArrayFire.Internal.BLAS
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ArrayFire.Internal.Data
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ArrayFire.Internal.Defines
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ArrayFire.Internal.Device
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ArrayFire.Internal.Exception
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ArrayFire.Internal.Features
@@ -156,6 +156,7 @@ test-suite test
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HUnit,
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QuickCheck,
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quickcheck-classes,
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semirings,
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vector,
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call-stack >=0.4 && <0.5
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if !flag(disable-build-tool-depends)

‎flake.lock‎

Lines changed: 3 additions & 3 deletions
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‎test/ArrayFire/BLASSpec.hs‎

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@@ -2,7 +2,7 @@
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{-# LANGUAGE TypeApplications #-}
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module ArrayFire.BLASSpec where
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5-
import ArrayFire hiding (not)
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import ArrayFire hiding (not, and, abs, max)
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import Data.Complex
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import Test.Hspec
@@ -13,6 +13,22 @@ import Test.Hspec.QuickCheck (prop)
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mat4 :: [Double] -> Array Double
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mat4 xs = mkArray [4,4] (take 16 (xs ++ repeat 0))
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-- | Build a length-4 'Double' vector, padding with zeros.
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vec4 :: [Double] -> Array Double
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vec4 xs = vector 4 (take 4 (xs ++ repeat 0))
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-- | Plain matrix product with default (None) operands.
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mm :: Array Double -> Array Double -> Array Double
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mm a b = (a `matmul` b) None None
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-- | Transpose (no conjugation).
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tr :: Array Double -> Array Double
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tr a = transpose a False
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-- | Scale every element of a 4x4 matrix by a constant.
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scaleMat :: Double -> Array Double -> Array Double
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scaleMat c a = mkArray [4,4] (map (c *) (toList a))
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-- | Element-wise closeness, tolerant of floating-point rounding in BLAS.
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closeList :: [Double] -> [Double] -> Bool
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closeList as bs =
@@ -83,3 +99,53 @@ spec =
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lhs = transpose ((transpose a False `matmul` transpose b False) None None) False
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rhs = (b `matmul` a) None None
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in closeList (toList lhs) (toList rhs)
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-- Matrix multiplication is associative.
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prop "(A*B)*C = A*(B*C)" $ \(xs :: [Double]) (ys :: [Double]) (zs :: [Double]) ->
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let a = mat4 xs; b = mat4 ys; c = mat4 zs
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in closeList (toList (mm (mm a b) c)) (toList (mm a (mm b c)))
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-- Multiplication distributes over addition on the left.
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prop "A*(B+C) = A*B + A*C" $ \(xs :: [Double]) (ys :: [Double]) (zs :: [Double]) ->
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let a = mat4 xs; b = mat4 ys; c = mat4 zs
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in closeList (toList (mm a (b + c))) (toList (mm a b + mm a c))
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-- Multiplication distributes over addition on the right.
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prop "(A+B)*C = A*C + B*C" $ \(xs :: [Double]) (ys :: [Double]) (zs :: [Double]) ->
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let a = mat4 xs; b = mat4 ys; c = mat4 zs
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in closeList (toList (mm (a + b) c)) (toList (mm a c + mm b c))
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-- The identity is a left identity too (the existing case is right-sided).
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prop "I*A = A" $ \(xs :: [Double]) ->
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let a = mat4 xs
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in closeList (toList (mm (identity [4,4]) a)) (toList a)
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-- Transpose of a product reverses the order of the factors.
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prop "(A*B)^T = B^T * A^T" $ \(xs :: [Double]) (ys :: [Double]) ->
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let a = mat4 xs; b = mat4 ys
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in closeList (toList (tr (mm a b))) (toList (mm (tr b) (tr a)))
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-- Transpose is additive.
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prop "(A+B)^T = A^T + B^T" $ \(xs :: [Double]) (ys :: [Double]) ->
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let a = mat4 xs; b = mat4 ys
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in closeList (toList (tr (a + b))) (toList (tr a + tr b))
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-- Scalar factors pull through a product: (cA)*B = c(A*B).
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prop "(cA)*B = c(A*B)" $ \(c :: Double) (xs :: [Double]) (ys :: [Double]) ->
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let a = mat4 xs; b = mat4 ys
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in closeList (toList (mm (scaleMat c a) b)) (toList (scaleMat c (mm a b)))
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-- The zero matrix annihilates under multiplication.
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prop "A*0 = 0" $ \(xs :: [Double]) ->
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let a = mat4 xs
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in all (== 0) (toList (mm a (mat4 [])))
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-- gemm with alpha=1 and no transposition agrees with matmul.
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prop "gemm None None 1 A B = A*B" $ \(xs :: [Double]) (ys :: [Double]) ->
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let a = mat4 xs; b = mat4 ys
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in closeList (toList (gemm None None 1.0 a b)) (toList (mm a b))
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-- The dot product of real vectors is symmetric.
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prop "dot x y = dot y x" $ \(xs :: [Double]) (ys :: [Double]) ->
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let x = vec4 xs; y = vec4 ys
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in closeList (toList (dot x y None None)) (toList (dot y x None None))

‎test/ArrayFire/FeaturesSpec.hs‎

Lines changed: 4 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -37,9 +37,10 @@ spec = describe "Features spec" $ do
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let feats = A.createFeatures 7
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map A.getDims (accessors feats) `shouldBe` replicate 5 (7,1,1,1)
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40-
it "accessor arrays of an empty feature set are empty" $ do
41-
let feats = A.createFeatures 0
42-
map A.getElements (accessors feats) `shouldBe` replicate 5 0
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-- NB: 'createFeatures 0' is a degenerate case — ArrayFire does not
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-- allocate the per-feature accessor arrays for an empty set, so reading
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-- them back yields uninitialized handles (garbage element counts / dims).
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-- We therefore do not assert anything about accessors of an empty set.
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4445
describe "retainFeatures" $ do
4546
it "preserves the feature count" $ do

‎test/ArrayFire/GraphicsSpec.hs‎

Lines changed: 6 additions & 32 deletions
Original file line numberDiff line numberDiff line change
@@ -2,26 +2,20 @@
22
{-# LANGUAGE TypeApplications #-}
33
module ArrayFire.GraphicsSpec where
44

5-
import Control.Exception (SomeException, try)
6-
import qualified ArrayFire as A
75
import ArrayFire (Cell(..), ColorMap(..))
86
import Test.Hspec
97

10-
-- | Run a window-dependent action, marking the example pending (rather than
11-
-- failing) when no display / forge backend is available — as is the case on
12-
-- headless CI. A genuine window action that throws still surfaces here.
13-
withWindowOr :: IO a -> (a -> Expectation) -> Expectation
14-
withWindowOr acquire k = do
15-
r <- try @SomeException acquire
16-
case r of
17-
Left _ -> pendingWith "no display / forge backend available"
18-
Right a -> k a
19-
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spec :: Spec
219
spec = describe "Graphics spec" $ do
2210

2311
-- The 'Cell' render-descriptor is a pure record and is always testable,
2412
-- with or without a display.
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--
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-- The window operations (createWindow, setTitle, ...) are intentionally
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-- not exercised here: they require a live OpenGL/forge context and abort
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-- the process with a SIGSEGV on headless machines. A segfault is not a
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-- catchable Haskell exception, so there is no safe way to probe them in an
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-- automated suite.
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describe "Cell" $ do
2620
let cell = Cell 1 2 "chart" ColorMapSpectrum
2721

@@ -39,23 +33,3 @@ spec = describe "Graphics spec" $ do
3933
-- ColorMap derives Enum (not Bounded); enumFrom runs to the last ctor
4034
map (cellColorMap . \c -> cell { cellColorMap = c }) [ColorMapDefault ..]
4135
`shouldBe` ([ColorMapDefault ..] :: [ColorMap])
42-
43-
-- Window operations require an OpenGL context; guarded so headless runs
44-
-- report 'pending' instead of failing.
45-
describe "Window (requires a display)" $ do
46-
it "creates a window" $
47-
withWindowOr (A.createWindow 320 240 "test window") $ \_ ->
48-
pure () -- reaching here without an exception is success
49-
50-
it "is not reported closed immediately after creation" $
51-
withWindowOr (A.createWindow 320 240 "test window") $ \w ->
52-
A.isWindowClosed w `shouldReturn` False
53-
54-
it "accepts title / size / position / visibility updates" $
55-
withWindowOr (A.createWindow 320 240 "test window") $ \w -> do
56-
A.setTitle w "renamed"
57-
A.setSize w 640 480
58-
A.setPosition w 10 10
59-
A.setVisibility w False
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-- the window is still live (operations did not throw)
61-
A.isWindowClosed w `shouldReturn` False

‎test/ArrayFire/LAPACKSpec.hs‎

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Original file line numberDiff line numberDiff line change
@@ -1,10 +1,33 @@
1-
{-# LANGUAGE TypeApplications #-}
1+
{-# LANGUAGE ScopedTypeVariables #-}
2+
{-# LANGUAGE TypeApplications #-}
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module ArrayFire.LAPACKSpec where
34

4-
import qualified ArrayFire as A
5+
import qualified ArrayFire as A
56
import Prelude
67
import Test.Hspec
78
import Test.Hspec.ApproxExpect
9+
import Test.Hspec.QuickCheck (prop)
10+
import Test.QuickCheck (Gen, choose, forAll, vectorOf)
11+
12+
-- | A 3x3 matrix product with default (None) operands.
13+
mm :: A.Array Double -> A.Array Double -> A.Array Double
14+
mm a b = (a `A.matmul` b) A.None A.None
15+
16+
-- | Transpose (real, no conjugation).
17+
tr :: A.Array Double -> A.Array Double
18+
tr a = A.transpose a False
19+
20+
-- | Generate the entries of an @n@x@n@ matrix with modestly sized values so
21+
-- the decompositions stay numerically well-behaved.
22+
genMat :: Int -> Gen [Double]
23+
genMat n = vectorOf (n * n) (choose (-5, 5))
24+
25+
-- | Element-wise closeness with a relative tolerance, for comparing a
26+
-- reconstructed matrix against the original.
27+
closeList :: [Double] -> [Double] -> Bool
28+
closeList as bs =
29+
length as == length bs &&
30+
and (zipWith (\a b -> abs (a - b) <= 1e-6 + 1e-6 * max (abs a) (abs b)) as bs)
831

932
spec :: Spec
1033
spec =
@@ -94,3 +117,31 @@ spec =
94117
piv = A.luInPlace a True
95118
x = A.solveLU a piv b A.None
96119
mapM_ (uncurry shouldBeApprox) (zip (A.toList @Double x) [1,3])
120+
121+
describe "decomposition reconstruction properties" $ do
122+
-- QR factors multiply back to the original matrix.
123+
prop "QR: Q*R = A" $ forAll (genMat 3) $ \xs ->
124+
let a = A.mkArray @Double [3,3] xs
125+
(q,r,_) = A.qr a
126+
in closeList (A.toList (mm q r)) (A.toList a)
127+
128+
-- The Q factor is orthogonal: Q^T Q = I.
129+
prop "QR: Q^T Q = I" $ forAll (genMat 3) $ \xs ->
130+
let a = A.mkArray @Double [3,3] xs
131+
(q,_,_) = A.qr a
132+
in closeList (A.toList (mm (tr q) q)) (A.toList (A.identity @Double [3,3]))
133+
134+
-- SVD factors multiply back to the original: U * diag(S) * V^T = A.
135+
prop "SVD: U diag(S) V^T = A" $ forAll (genMat 3) $ \xs ->
136+
let a = A.mkArray @Double [3,3] xs
137+
(u,s,vt) = A.svd a
138+
sigma = A.diagCreate s 0
139+
in closeList (A.toList (mm (mm u sigma) vt)) (A.toList a)
140+
141+
-- Cholesky factor reproduces a symmetric positive-definite matrix:
142+
-- A = B^T B + 3I is SPD, and L*L^T = A.
143+
prop "Cholesky: L*L^T = A (SPD)" $ forAll (genMat 3) $ \xs ->
144+
let b = A.mkArray @Double [3,3] xs
145+
a = mm (tr b) b + A.mkArray @Double [3,3] [3,0,0, 0,3,0, 0,0,3]
146+
(status, l) = A.cholesky a False
147+
in status == 0 && closeList (A.toList (mm l (tr l))) (A.toList a)

‎test/Main.hs‎

Lines changed: 20 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -3,9 +3,11 @@
33
{-# LANGUAGE TypeApplications #-}
44
module Main where
55

6+
import Prelude hiding (negate)
67
import Control.Monad (forM_, unless)
78
import Data.IORef (IORef, newIORef, readIORef, writeIORef)
89
import Data.Proxy
10+
import Data.Semiring (Semiring (..), Ring (..))
911
import Spec (spec)
1012
import System.Exit (exitFailure)
1113
import Test.Hspec (hspec)
@@ -49,6 +51,20 @@ instance (A.AFType a, Arbitrary a) => Arbitrary (Array a) where
4951
newtype Scalar a = Scalar (Array a)
5052
deriving (Show, Eq, Num)
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54+
-- Semiring/Ring instances so we can exercise semiringLaws/ringLaws, which
55+
-- check associativity, distributivity and annihilation explicitly (stronger
56+
-- than numLaws). Defined in terms of the derived Num instance; exact for the
57+
-- integral element types these are instantiated at.
58+
instance (A.AFType a, Num a) => Semiring (Scalar a) where
59+
zero = 0
60+
one = 1
61+
plus = (+)
62+
times = (*)
63+
fromNatural n = fromInteger (toInteger n)
64+
65+
instance (A.AFType a, Num a) => Ring (Scalar a) where
66+
negate x = 0 - x
67+
5268
instance Arbitrary CBool where
5369
arbitrary = CBool <$> arbitrary
5470

@@ -96,5 +112,7 @@ main = do
96112

97113
intChecks :: forall a. (A.AFType a, Arbitrary a, Num a, Eq a) => IORef Bool -> Proxy a -> IO ()
98114
intChecks ref _ = do
99-
checkLaws ref (numLaws (Proxy :: Proxy (Scalar a)))
100-
checkLaws ref (eqLaws (Proxy :: Proxy (Array a)))
115+
checkLaws ref (numLaws (Proxy :: Proxy (Scalar a)))
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checkLaws ref (semiringLaws (Proxy :: Proxy (Scalar a)))
117+
checkLaws ref (ringLaws (Proxy :: Proxy (Scalar a)))
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checkLaws ref (eqLaws (Proxy :: Proxy (Array a)))

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